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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

Hello!!!

Could you help me at the following exercise?

Let

and that each solution of the differential equation has the form:.

*Last edited by evinda (2013-12-11 06:37:39)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

Hi;

The Wronskian is

I do not see how to use v1 and v2?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi

I think evinda is referring to this:Wronskian.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

I used the one in Mathematica, they should be the same thing.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

The Wronskian is

|u(0) v(0)|

|u'(0) v'(0) |

But...how can I show that there are constants

*Last edited by evinda (2013-12-11 09:27:13)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

What functions are u and v? They are not defined.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Well, here they are called v1 and v2 instead of u and v. Does not change much.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

What is v1 and v2?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

They are two solutions of the differential equation for which it's true that v1/v2 is not constant.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

That would require solving the DE. Since when do you need the solve the DE to get the Wronskian?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

anonimnystefy wrote:

They are two solutions of the differential equation for which it's true that v1/v2 is not constant.

Exactly!!The Wronskian is:

| v1(0) v2(0) |

| v1'(0) v2'(0) |

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

bobbym wrote:

That would require solving the DE. Since when do you need the solve the DE to get the Wronskian?

Which DE do you mean that I have to solve??

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

When I solve the DE, I get an answer that has to arbitrary constants s1 and c2

I can not eliminate them without some more information.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

bobbym wrote:

That yields a Wronskian of

Now what?

I haven't understood..Do you mean that I have to take the derivative of the Wronskian and solve the DE or which DE do you mean??

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

This DE, y''+ay'+by=0

If v1 and v2 are solutions of that DE then you have to solve the DE to get the solutions. I have already done that.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

I found the Characteristic equation,that is

that has discriminant withSo,

Am I right so far?And how can I continue?

*Last edited by evinda (2013-12-11 10:10:12)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

I am not getting that as a solution to the DE. Where is c1 and c2 in your solution?

Did you copy the question correctly?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi evinda

Those are the solutions, but I don't think you are supposed to use them.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

Shouldn't you have use the roots rather than the discriminant?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

bobbym wrote:

I am not getting that as a solution to the DE. Where is c1 and c2 in your solution?

Did you copy the question correctly?

Yes,I copied the question correcty..Should I have used

and instead of c_{1} and ?*Last edited by evinda (2013-12-11 10:14:50)*

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

anonimnystefy wrote:

Hi evinda

Those are the solutions, but I don't think you are supposed to use them.

But???How else can I start???

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

bobbym wrote:

Shouldn't you have use the roots rather than the discriminant?

Where do you mean?At the general solution?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,380

This is what I am getting for a solution to that DE:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

evinda wrote:

I found the Characteristic equation,that is

that has discriminant with

So,Am I right so far?And how can I continue?

So is she.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

And how can I continue now??

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